In digital transmission over dispersive channels, such as the mobile communication channel or wire pairs, the transmit signal is distorted and impaired by noise. Consequently, in the receiver special measures are necessary to recover the transmitted data from the received signal, i.e., an equalization method has to be applied. The optimum technique for equalization of dispersive channels is maximum-likelihood sequence estimation (MLSE) which is described in G. D. Forney, Jr. “Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference”, IEEE Transactions on Information Theory, IT-18, 363–378, May 1972, and which can be implemented using the Viterbi algorithm. However, for long channel impulse responses and/or non-binary signal constellations the Viterbi algorithm is not applicable because here a large computational complexity results. Therefore, in these cases, suboptimum reduced-state sequence estimation (RSSE) methods, as described in M. V. Eyuboglu, S. U. Qureshi “Reduced-State Sequence Estimation with Set Partitioning and Decision Feedback”, IEEE Trans. on Communication, COM-36, 13–20, January 1988, or Decision-Feedback Sequence Estimation (DFSE), as described in A. Duel-Hallen, C. Heegard “Delayed Decision-Feedback Sequence Estimation”, IEEE Trans. on Communications, COM-37, 428–436, May 1989, have to be employed.
All methods cited above are optimized for the case where the received signal is impaired by additive white Gaussian noise (AWGN). In the presence of additional disturbances due to interference it has to be expected that these methods degrade severely because of metric mismatch and a too high disturbance variance. Disturbances due to interference become more and more important in mobile communication systems and in wire pair systems. A degradation of power efficiency results for both adjacent channel interference (ACI) and cochannel interference (CCI, i.e., signal and interference occupy the same frequency band) if no additional measures are taken. Prior to equalization the interference should be significantly reduced by an appropriate pre-processing technique to make the remaining impairment as small as possible and white. Since in a block transmission method the spectral characteristic of the interference varies from block to block, the pre-processing has to be adjusted in each block. An appropriate pre-processing strategy was proposed in S. Ariyavisitakul, J. H. Winters, N. R. Sollenberger “Joint Equalization and Interference Suppression for High Data Rate Wireless Systems”, in Proceedings of Vehicular Technology Conference (VTC '99 Spring), 700–706, Houston, Tex., 1999. However, with this strategy a high performance can only be achieved for diversity reception, i.e., at least two receive antennas are necessary.
It is well known that transmission over a dispersive intersymbol interference (ISI) producing channel with pulse amplitude modulation (PAM) can be modeled as a discrete-time system as depicted in FIG. 1. The general case with N fold diversity (N≧1) at the receiver is considered, while mono reception (N=1) results as a special case. After sampling at symbol rate 1/T, the received signals are given by the convolution of the transmitted PAM sequence a[k] with the impulse response hi[k] of length Li of the channel pertaining to the ith antenna, impaired by discrete-time noise:
                                                        r              i                        ⁡                          [              k              ]                                =                                                    ∑                                  κ                  =                  0                                                                      L                    i                                    -                  1                                            ⁢                                                                    h                    i                                    ⁡                                      [                    κ                    ]                                                  ⁢                                  a                  ⁡                                      [                                          k                      -                      κ                                        ]                                                                        +                                          n                i                            ⁡                              [                k                ]                                                    ,                  i          ∈                      {                          1              ,              2              ,              …              ⁢                                                          ,              N                        }                                              (        1        )            
Depending on the adopted modulation method the amplitude coefficients a[k] and the channel impulse responses hi[k] are either purely real, purely imaginary, or complex. With respect to the invention, in the following, we only consider modulation methods whose amplitude coefficients can be modeled at the receiver as purely real, purely imaginary, or as lying on an arbitrary straight line in the complex plane. E.g. binary continuous phase modulation (CPM) methods, which are often used in mobile communication systems due to their bandwidth efficiency and their low peak-to-average power ratio, can be approximately described by PAM signals as outlined in P. A. Laurent “Exact and approximate construction of digital phase modulations by superposition of amplitude modulated pulses (AMP)”, IEEE Trans. on Commun., COM 34, 150–160, 1986. The discrete-time disturbance ni[k] consists of two componentsni[k]=niAWGN[k]+niINT[k],   (2)where niAWGN[k] refers to the AWGN component, which has zero mean and is Gaussian distributed and white (the latter is true if a whitened matched filter, as described in G. D. Forney, Jr. “Maximum-Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference”, IEEE Transactions on Information Theory, IT-18, 363–378, May 1972, or a general square-root Nyquist filter is used as continuous-time receiver input filter prior to sampling). The disturbance by niAWGN[k] is mainly due to thermal noise in the receiver. niINT[k] is the disturbance due to interference,
                                                        n              i              INT                        ⁡                          [              k              ]                                =                                    ∑                              μ                =                1                            L                        ⁢                                          ∑                                  κ                  =                  0                                                                      L                                          i                      ,                      μ                                        INT                                    -                  1                                            ⁢                                                                    h                                          i                      ,                      μ                                        INT                                    ⁡                                      [                    κ                    ]                                                  ⁢                                                      a                    μ                    INT                                    ⁡                                      [                                          k                      -                      κ                                        ]                                                                                      ,                  i          ∈                                    {                              1                ,                2                ,                …                ⁢                                                                  ,                N                            }                        .                                              (        3        )            
Here,
      h          i      ,      μ        INT    ⁡      [    κ    ]  refers to the channel impulse response from the μth interferer to receive antenna i and
  L      i    ,    μ    INTis the corresponding impulse response length. The general case with I interferers, whose data symbols are denoted by
            a      μ      INT        ⁡          [      κ      ]        ,is considered. With respect to the invention, again modulation methods with purely real or purely imaginary amplitude coefficients, or amplitude coefficients which lie on a straight line in the complex plane, are exclusively presumed. Since purely imaginary amplitude coefficients and amplitude coefficients which lie on an arbitrary straight line can be transformed into purely real amplitude coefficients by a simple phase rotation, in the following, only the latter case will be considered.
If the continuous-time received signals of the different antennas are fractionally-spaced sampled with sample frequency K/T (K: oversampling factor, e.g. K=2), in principle, the same model results. In this case, the discrete-time received signals of the different antennas can be represented by K symbol-rate (1/T) polyphase components. Consequently, the number of discrete-time symbol-rate received signals is increased to N·K. Therefore, in principle, the following considerations are also applicable for fractionally-spaced sampling. In principle, there are two different approaches for reconstruction of the transmitted symbols, cf. e.g. C. Tidestav, M. Sternad, A. Ahlen “Reuse Within a Cell—Interference Rejection or Multiuser Detection”, IEEE Trans. on Commun., COM-47, 1511–1522, October 1999. For the first approach the principles of multiuser detection are employed, i.e., the symbol sequences a[•] and
            a      μ      INT        ⁡          [      ·      ]        ,      μ    ∈                  {                  1          ,          2          ,          …          ⁢                                          ,          I                }                                are jointly estimated (joint maximum-likelihood sequence estimation). In the expressions for the symbol sequences the dot [•] indicates the entire symbol sequence a[k], with −∞<k<+∞.
With this approach the optimum estimation quality can be achieved. Unfortunately, the required computational complexity for the joint (or iterative) estimation is very high. In addition, for this approach the channel impulse responses
      h          i      ,      μ        INT    ⁡      [    κ    ]  are required, whose estimation is very difficult, since, in general, the receiver does not have knowledge about the training sequences of the interfering signals and also the temporal position of the training sequences is unknown, cf. e.g. B. C. Wah Lo, K. Ben Letaief “Adaptive Equalization and Interference Cancellation for Wireless Communication Systems”, IEEE Trans. on Commun. COM-47, 538–545, April 1999. For these reasons the second approach, where interference suppression with subsequent equalization is performed, is more promising. A method based on this approach was proposed in S. Ariyavisitakul, J. H. Winters, N. R. Sollenberger “Joint Equalization and Interference Suppression for High Data Rate Wireless Systems”, in Proceedings of Vehicular Technology Conference (VTC '99 Spring), 700–706, Houston, Tex., 1999. Thereby the N different discrete-time received signals ri[k] are filtered separately and the filter output signals are combined, cf. FIG. 1. Subsequently, equalization is performed, e.g. MLSE, RSSE, DFSE or DFE (decision-feedback equalization). The resulting block diagram of the receiver is depicted in FIG. 1. The signal after feedforward filtering and combining is given by
                              s          ⁡                      [            k            ]                          =                              ∑                          i              =              1                        N                    ⁢                                    ∑                              κ                =                0                                                              L                  i                  f                                -                1                                      ⁢                                                            f                  1                                ⁡                                  [                  κ                  ]                                            ⁢                                                r                  i                                ⁡                                  [                                      k                    -                    κ                                    ]                                                                                        (        4        )            
The ith filter for filtering of the received sequence ri[k] is shown in detail in FIG. 2. The optimization of the filter impulse responses fi[k] of lengths Liƒcan be e.g. accomplished using a multiple-input single-output minimum mean-squared error decision-feedback equalizer (MISO MMSE-DFE), whose structure is depicted in FIG. 3. Thereby, thick lines and thin lines refer to complex-valued and real-valued signals and systems, respectively. For the special case of a single receive antenna (N=1) the resulting structure is depicted in FIG. 4. In the DFE the complex-valued impulse responses fi[k] are the feedforward filters and have to be adaptively jointly optimized with the complex-valued feedback filter b[k]. When the adaptation process is completed, the feedforward filter coefficients are carried over to the structure according to FIG. 1. If the filter lengths are chosen sufficiently large, after the combination the interference is significantly reduced and, in addition, the total disturbance at this point is approximately white and Gaussian distributed and, therefore, the subsequent application of trellis-based equalization techniques is justified.
A closed-form solution for calculation of the prefilters, as e.g. proposed in EP 99 301 299.6 for calculation of the prefilter for DFSE/RSSE and disturbance by white noise, cannot be applied. For this, not only the impulse responses hi[k] but also the impulse responses of the interfering signals hi,μINT[κ] would have to be known. However, the latter cannot be easily estimated since, in general, the training sequences of the interfering signals are not known at the receiver. Therefore, filter calculation has to be performed using a recursive adaptive algorithm. In S. Ariyavisitakul, J. H. Winters, N. R. Sollenberger “Joint Equalization and Interference Suppression for High Data Rate Wireless Systems”, Proceedings of Vehicular Technology Conference (VTC'99 Spring), 700–706, Houston, Tex., 1999, the application of the recursive-least squares (RLS) algorithm was proposed for filter optimization, cf. also S. Haykin “Adaptive Filter Theory”, Prentice Hall, Upper Saddle River, N.J., third edition, 1996. A significant disadvantage of this approach is that high performance cannot be achieved in case of mono reception (N=1). The main reason for this is that in this case an interfering signal cannot be sufficiently suppressed. With reference to FIG. 3, for N=2 the signals r1[k] and r2[k] comprise the respective received signal and noise, where the interfering signals are contained in the noise. Adjusting the filter coefficients suitably, the interfering signals may cancel each other. For N=1 there is only one received signal and, therefore, cancellation is not possible, of course.